Question

A powder tin has a square base with side 12 cm and height 17.5 cm. Another is cylindrical with diameter of its base 12 cm and height 17.5 cm. Which has more capacity and by how much?

Answer 1

Length of the powder tin =12 cm
Breadth of the powder tin =12 cm
Height of the powder tin =17.5 cm

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{powder}\mathrm{tin}=l\times b\times h \\ =12\times 12\times 17.5{\mathrm{cm}}^3 \\ =2520{\mathrm{cm}}^3 \end{gathered}$$

Now, radius of the cylinder = 6 cm
Height of the cylinder = 17.5 cm
$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{22}{7}\times 6^2\times 17.5 \\ =1980{\mathrm{cm}}^3 \end{gathered}$$

∴ The capacity of the powder tin is more than that of the cylinder by (2520 $-$1980) cm³ = 540 cm³